Thermodynamic process P^2+aV^2=constant

[rafaelgm9]

Homework Statement

One mole of ideal gas expands from an initial volume V₁,to a final volume V₂. Where V₁ and P₁ correspond to the volume and initial gas pressure, whereas V₂ and P₂ correspond to the volume and pressure at the end of the process. The process is described by the equation:
P²+aV²=constant
Find the work donde by the gas as a function of P₁, P₂, V₁, V₂. ΔP/P<<1 and ΔV/V<<1.

Homework Equations

P²+aV²=constant
W=∫PdV

The Attempt at a Solution

i tried to find P as a function of V but then i got a weird result.

 

[voko]

You will have to show what you have tried to get help here.